2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227582Classes of polynomial differential equations of degree n are considered. An explicit upper bound on the size of the coefficients are given which implies that each equation in the class has exactly n complex periodic solutions. In most of the classes the upper bound can be improved when we consider real periodic solutions. We present a proof to a recent conjecture on the number of periodic solutions. The results are used to give upper bounds for the number of limit cycles of polynomial two-dimensional systems.15 pagesClassical Analysis and ODEsDynamical Systems34C25; 34C07; 34C05text